Related papers: An introduction to multiple orthogonal polynomials…

We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of…

We discuss asymptotic properties of a family of discrete probability measures which may be used to model particle configurations with a wall on a set of discrete nodes. The correlations are shown to be determinantal and are expressed in…

We introduce a monic polynomial p_N(z) of degree N whose coefficients are the zeros of the N-th degree Hermite polynomial. Note that there are N! such different polynomials p_N(z), depending on the ordering assignment of the N zeros of the…

Systems of orthogonal polynomials whose recurrence coefficients tend to infinity are considered. A summability condition is imposed on the coefficients and the consequences for the measure of orthogonality are discussed. Also discussed are…

This work explores classical discrete multiple orthogonal polynomials, including Hahn, Meixner of the first and second kinds, Kravchuk, and Charlier polynomials, with an arbitrary number of weights. Explicit expressions for the recursion…

The weak convergence of orthogonal polynomials is given under conditions on the asymptotic behaviour of the coefficients in the three-term recurrence relation. The results generalize known results and are applied to several systems of…

We consider a uniform distribution on the set $\mathcal{M}_k$ of moments of order $k \in \mathbb{N}$ corresponding to probability measures on the interval $[0,1]$. To each (random) vector of moments in $\mathcal{M}_{2n-1}$ we consider the…

Given multiple orthogonal polynomials on the real line with respect to a system $\bm{\mu} = (\mu_1,\ldots,\mu_r)$, we investigate multiple orthogonal polynomials associated with any rational perturbation of the form $$…

We utilize Cauchy's argument principle in combination with the Jacobian of a holomorphic function in several complex variables and the first moment of a ratio of two correlated complex normal random variables to prove explicit formulas for…

We combine functional analytic and geometric viewpoints on approximate Birkhoff and isosceles orthogonality in generalized Minkowski spaces which are finite-dimensional vector spaces equipped with a gauge. This is the first approach to…

A Nikishin-Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.

We develop a theory of Sobolev orthogonal polynomials on the Sierpi\'nski gasket ($SG$). These orthogonal polynomials arise through the Gram-Schmidt orthogonalisation process applied on the set of monomials on $SG$ using several notions of…

Recursive algebraic construction of two infinite families of polynomials in $n$ variables is proposed as a uniform method applicable to every semisimple Lie group of rank $n$. Its result recognizes Chebyshev polynomials of the first and…

It is well-known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation is orthogonal with respect to some positive Borel…

In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well…

Many symmetric orthogonal polynomials $(P_n(x))_{n\in\mathbb{N}_0}$ induce a hypergroup structure on $\mathbb{N}_0$. The Haar measure is the counting measure weighted with $h(n):=1/\int_\mathbb{R}\!P_n^2(x)\,\mathrm{d}\mu(x)\geq1$, where…

We introduce and study a general notion of polynomial functor from a small monoidal symmetric category whose unit is an initial object and give a classification result of polynomial functors of degree smaller of equal to n modulo those of…

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of…

We obtain Plancherel-Rotach type asymptotics valid in all regions of the complex plane for orthogonal polynomials with varying weights of the form $e^{-NV(x)}$ on the real line, assuming that $V$ has only two Lipschitz continuous…

Inspired by the works in [1] and [8] we introduce what we call $k$-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This…